Geodesic
On convergence conditions for Dirichlet series on closed polygons
Sbornik. Mathematics, Tome 24 (1974) no. 4, pp. 463-481 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper treats the questions of convergence and summability on a convex polygon $Q$ of the Dirichlet series of a function $f(z)$ which is analytic in $Q$ and continuous on $\overline Q$. Necessary and sufficient conditions for convergence are given for the case of a square; in the general case, if the necessary conditions for convergence are satisfied, it is sufficient that the integral $\int_0^1\frac{\omega(f;t)}t\,dt$ converge. Bibliography: 7 titles. 
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     author = {V. K. Dzyadyk},
     title = {On convergence conditions for {Dirichlet} series on closed polygons},
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V. K. Dzyadyk. On convergence conditions for Dirichlet series on closed polygons. Sbornik. Mathematics, Tome 24 (1974) no. 4, pp. 463-481. http://geodesic.mathdoc.fr/item/SM_1974_24_4_a0/

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